Abstract
The motion and decay of circular vortex rings with an inner viscous core is considered by systematic matching of inner and outer asymptotic expansions. The governing Navier-Stokes equations are reduced to a coupled integro-differential system. A method of construction of solutions for the integro-differential system is presented. The initial vorticity distribution may be non-similar. Also presented is a method for introducing a time shift which makes the first term in the series solution for the vorticity to be the “best” approximation. The analysis is then applied to the motion and decay of a pair of coaxial vortex rings.
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